Beside, the popular K-means clustering can be considered as solving an optimization problem that comes up in the quantization problem, a simple but very practical connection [1]}, [2]}. The connection is as follows: Given \(m\)  unlabeled data \(x^{\prime }_1, . . . , x^{\prime }_m \in \theta \) . Suppose
that these data are related to at most \(k\)  clusters where \(k \ge 1\)  is a given number. The K-means problem finds
the set \(Z\)  containing at most \(k\)  atoms \(\theta _1, . . . , \theta _k \in \theta \)  that minimizes: \(\inf _{Z:|Z| \le k}{\frac{1}{m} \sum _{i=1}^m d^2(x^{\prime }_i,Z)}\) .
